Dynamic versus Static Structure Functions and Novel Diffractive Effects in QCD Page: 3 of 8
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Static Dynamic
* Square of Target LFWFs Modified by Rescattering: ISI & FSI
* No Wilson Line Contains Wilson Line, Phases
* Probability Distributions No Probabilistic Interpretation
* Process-Independent Process-Dependent - From Collision
* T-even Observables T-Odd (Sivers, Boer-Mulders, etc.)
* No Shadowing, Anti-Shadowing Shadowing, Anti-Shadowing, Saturation
* Sum Rules: Momentum and J= Sum Rules Not Proven
* DGLAP Evolution; mod. at large x DGLAP Evolution
* No Diffractive DIS Hard Pomeron and Odderon Diffractive DIS
quark fiaste
proton
FIGURE 1. Static versus dynamic structure functions
currents. In fact, Schienbein et al. [7] have recently given a comprehensive analysis of
charged current deep inelastic neutrino-iron scattering, finding significant differences
with the nuclear corrections for electron-iron scattering.
It is thus important to distinguish "static" structure functions which are computed
directly from the LFWFs of the target from the "dynamic" empirical structure functions
which take into account rescattering of the struck quark. Since they derive from the LF
eigenfunctions of the target hadron, the static structure functions have a probabilistic
interpretation. Since the wavefunction of a stable eigenstate is real, the static structure
functions do not describe DDIS nor the single-spin asymmetries discussed below since
such phenomena involves the complex phase structure of the y*p amplitude. One can
augment the light-front wavefunctions with a gauge link corresponding to an external
field created by the virtual photon qq pair current [8, 9], but such a gauge link is
process dependent [10], so the resulting augmented wavefunctions are not universal.
[3, 8, 11]. We emphasize that the shadowing of nuclear structure functions is due to
the destructive interference between multi-nucleon amplitudes involving diffractive DIS
and on-shell intermediate states with a complex phase. The physics of rescattering
and shadowing is thus not included in the nuclear light-front wavefunctions, and a
probabilistic interpretation of the nuclear DIS cross section is precluded. The distinction
between static structure functions; i.e., the probability distributions computed from
the square of the light-front wavefunctions, versus the nonuniversal dynamic structure
functions measured in deep inelastic scattering is summarized in fig. 1.
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Brodsky, Stanley J. Dynamic versus Static Structure Functions and Novel Diffractive Effects in QCD, article, November 12, 2008; [Menlo Park, California]. (https://digital.library.unt.edu/ark:/67531/metadc895794/m1/3/: accessed March 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.